In Prof. Leahy's class, if a student does homework most days, the chance of passing the course is 90%. On the other hand, if a student does not do homework most days, the chance of passing the course is only 30%. Prof. Leahy claims that 70% of his students do homework on a regular basis. If a student is chosen at random from Prof. Leahy's class, find the following probabilities:
a. p(the student did not do homework and he/she passed the course)
b. p(the student did not do homework given that she/he passed the course)
Answers
Answer:
a) p(the student did not do homework and he/she passed the course) = 0.09
b) p(the student did not do homework given that she/he passed the course) = 0.125.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)
In which
P(B|A) is the probability of event B happening, given that A happened.
\(P(A \cap B)\) is the probability of both A and B happening.
P(A) is the probability of A happening.
a. p(the student did not do homework and he/she passed the course)
If a student does not do homework most days, the chance of passing the course is only 30%. 100 - 70 = 30% don't do homework on a regular basis.
So
0.3*0.3 = 0.09
p(the student did not do homework and he/she passed the course) = 0.09
b. p(the student did not do homework given that she/he passed the course)
Conditional probability.
Event A: Passed the course
Event B: Did not do homework.
p(the student did not do homework and he/she passed the course) = 0.09
This means that \(P(A \cap B) = 0.09\)
Probability that the student passes the course:
90% of 70%(do homework)
30% of 30%(do not do homework).
This means that:
\(P(A) = 0.9*0.7 + 0.3*0.3 = 0.72\)
p(the student did not do homework given that she/he passed the course)
\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.09}{0.72} = 0.125\)
So
p(the student did not do homework given that she/he passed the course) = 0.125.
Related Questions
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer:
B. 3188.5 cubic inches.
Step-by-step explanation:
The volume of a cone is calculated using the following formula:
Volume = (1/3) * π * r² * h
Where:
π is the mathematical constant pi, approximately equal to 3.14.r is the radius of the base of the cone.h is the height of the cone.In this problem, we are given that r = 17 inches and S.h = 20 inches.
First we need to find height h.
py using Pythagorous theorem,we get
c²=a²+b²
here c= slight height and a is radius
20²=17²+b²
20²-17²=b²
111=b²
b=√(111)
Plugging these values into the formula, we get:
Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches
Therefore, the volume of the cone is 3188.5 cubic inches.
From a point 340 feet away from the base of the Peachtree Center Plaza in Atlanta, Georgia, the angle of elevation to the top of the building is 65°. Find the height of
the building. (Hint: The angle of elevation is from the ground up to the top of the
building!)
Answers
Solution:
Given data:
Distance from a point to the Peachtree Center Plaza in Atlanta, Georgia (base) = 340 feet
The angle of elevation to the top of the building = 65°
To find height of the building (perpendicular- p):
tan thetha = p/b
Tan 65°= h/340
tan 65°=2.144507
Now,
h= tan 65° * 340
= 2.144507 * 340
= 729.132 feet
So, the height of the building is 729.132 feet
Complete the truth table for the given statement by filling in the required columns.
Answers
Answer:
-P is true.
Step-by-step explanation:
q v-p is false.
A woman deposits $300 in a savings account that pays 6% annually. If she withdraws all the money in the account after 120 days, how much does she withdraw (rounded to the nearest dollar)?
Answers
The woman will withdraw $300 given 6% interest rate annually.
We can use the formula for simple interest to solve this problem:
I = Prt
where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:
r = 0.06/365 = 0.00016438356
The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:
I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999
The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:
300 + 0.017 = $300.02
Rounding to the nearest dollar, the woman will withdraw $300.
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What to do when customer hands you a dime for full change in dollars back?
Answers
Answer:
If you are using a cash register, giving back correct change is pretty simple. Just type in the cost of the item and the amount paid and bingo, the cash register tells you how much change to give back. However, if your cash register is broken, or you entered the wrong amount, or you don’t have a cash register, you’ll need to know how to make change on your own. The basic method is to count up from the price of the purchase to the amount the customer paid.
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What is the perimeter of the shape below? Use 3.14 for pi. Answer with numbers only, no units.
DO NOT ROUND THE ANSWER
Answers
Step-by-step explanation:
The circumference of a WHOLE circle = pi * d
you have 1/2 of this and d = 10 ft
so 1/2 pi * 10 PLUS the two straight sides + 8+6
1/2 pi * 10 + 8 + 6
5 pi + 8 + 6
5 * 3.14 + 14 = 29.7 ft
Rearrange the following words to make a sentence:
opposite is direction north east the of
Is the statement true or false? This question is required. *
Answers
The rearrangement of Tue following words to make a meaningful sentence is as follows:
The direction is opposite of the north east.The statement is true or false.What is a sentence?A sentence is defined as the a group of words that is made up of a subject, a verb and punctuation marks which are used to create a meaning to the sentence.
The restructuring of the given sentence above would be shown below as follows:
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H. W 3: If you have a sample space S= {1,2,3,4,5,6,7}, A={1,2,4,5,7}, B={1,2} and C={4,6}, describe it by Venn diagram.
Answers
Answer:so the answer is 1,9,7,3,5,2
Step-by-step explanation:
The set of all possible outcomes is S = {A, C, G, T}. The set of all possible outcomes is also called the sample space. Events of interest might be E1 = an A
f there are 60 seconds in an minute, 60 minutes in an hour, 24 hours in a day, and 7 days in a week, how many seconds are in a week? Hint: Use a calculator to solve this problem.
Answers
Answer:
604800
Step-by-step explanation:
2) If the third term of a geometrical progression is 18 and the fifth term is 1162, find the common ratio
Answers
The common ratio in the sequence is √581/3
How to find the ratio?We know that in a geometrical progression with a common ratio R, the recursive formula is:
A(n) = R*A(n - 1)
That means that each term in the sequence is R times the previous term, so knowing one term and R (or two terms) we can completely define the sequence.
Here we know that:
A(3) = 18
A(5) = 1162
Then we could write:
A(5) = R^2*A(3)
1162 = 18*R^2
1162/18 = R^2
581/9 = R^2
√(581/9) = R
√581/3 =R
That is the common ratio.
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How can renaming numbers help you solve this problem?
Answers
Solve the problem using decimal multiplication
Given a mean of 34 and a standard deviation of 5. Find the following z-scores.
Answers
The z-score for the raw score of 39 is 1.The z-score for the raw score of 30 is -0.8.Z-scores measure the number of standard deviations a raw score is from the mean. A positive z-score indicates a raw score above the mean, while a negative z-score indicates a raw score below the mean.
To find the z-scores, we need to use the formula:
z = (x - μ) / σ
where:
z is the z-score,x is the raw score,μ is the mean, andσ is the standard deviation.
Let's calculate the z-scores for the given mean of 34 and standard deviation of 5.For a raw score of 39:
z = (39 - 34) / 5
z = 5 / 5
z = 1
So, the z-score for the raw score of 39 is 1.For a raw score of 30:
z = (30 - 34) / 5
z = -4 / 5
z = -0.8
The z-score for the raw score of 30 is -0.8.
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Which fractions equal the whole number 3?
Answers
Answer:
9/3=3
Step-by-step explanation:
3 goes into 9 3 times
3,6,9
Studying for my math final tomorrow just need to make sure I’m doing it right
Answers
Evaluate. 12⋅(1\4+1\3)^2+2\3 Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
I'm confused, I'm not sure if the 12 you added to the problem is like the number of the problem or part of the problem, but my answer is going to be with the 12 as part of the problem.
Answer: 19/4 or 4 3/4 or 4.75
Step-by-step explanation: First you have to use the PEMDAS, which means first you have to do the parenthesis first, so add the 1/4 to the 1/3 which equals 7/12. so do that to the second power and then multiply the 12 and add the 2/3 which gets you 19/4
A company’s cereal boxes advertise that each box contains 9.65 ounces of cereal. In fact, the amount of cereal in a randomly selected box follows a Normal distribution with mean μ = 9.70 ounces and standard deviation σ = 0.03 ounce. Now take an SRS of 5 boxes. What is the probability that the mean amount of cereal in these boxes is less than 9.65 ounces?
What is the probability that the mean amount of cereal ¯
in 5 randomly selected boxes is at most 9.65?
Answers
The probability that the mean amount of cereal in 5 randomly selected boxes is at most 9.65 ounces is 0.4808.
What is the probability?The Central limit theorem is used to find the probability
Data given:
sample size = 5.
mean, μ = 9.70 ounces
standard deviation, σ = 0.03 ounce.
To calculate the probability, we determine the z-score corresponding to the sample mean of 9.65 ounces using the z-score formula.
z = (x - μ) / (σ / √n)wherex is the sample mean,
μ is the population mean,
σ is the population standard deviation, and
n is the sample size.
For the sample mean of 9.65 ounces in 5 boxes:
z = (9.65 - 9.70) / (0.03 / √5)
z ≈ -0.05 / (0.03 / √5)
Using a calculator, we find that the probability is approximately 0.4801.
Therefore, the probability that the mean amount of cereal in 5 randomly selected boxes is less than 9.65 ounces is approximately 0.4801.
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Someone help please!!!
Answers
The answer is 4(6+3) because it also equals 36.
Find the product
3(z+4)(x-5)
Answers
Answer:
3zx-15z+12x-60
Step-by-step explanation:
first do parenthesis and distribute (z+4)(x-5) into zx-5z+4x-20
then distribute the 3 to get the answer
Andre ran 2 kilometers in 15 minutes and Jada ran 3 kilometers in 20 minutes. Both ran at a constant speed. Did they run the same rate? Explain or show your reasoning.
You might use:
-ratio tables
-double number lines
-unit rates
-Equivalent ratios
yeah
Answers
Answer:
no, Andre ran at a sperm of 8km/hr while jada ran at 9km/hr you can find that by Andre going 2km in 15 minutes which turns to hours by multiplying by 4/4 to get 8/60 which 60 minutes is 1 hour then jada multiply by 3/3 which would be 9/60
6.1.3
What requirements are necessary for a normal probability distribution to be a standard normal probability distribution?
Answers
Answer:
The requirements that are necessary for a normal probability distribution to be a standard normal probability distribution are µ = 0 and σ = 1.
Step-by-step explanation:
A normal-distribution is an accurate symmetric-distribution of experimental data-values.
If we create a histogram on data-values that are normally distributed, the figure of columns form a symmetrical bell shape.
If X \(\sim\) N (µ, σ²), then \(Z=\frac{X-\mu}{\sigma}\), is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z \(\sim\) N (0, 1).
The distribution of these z-variates is known as the standard normal distribution.
Thus, the requirements that are necessary for a normal probability distribution to be a standard normal probability distribution are µ = 0 and σ = 1.
A city in Texas started the day at -5 degrees Fahrenheit. The temperature increased by 15.1 degrees by nightfall. What is the final temperature at nightfall?
Answers
Step-by-step explanation:
Add 15.1 to -5-5 + 15.1 = 10.1Answer:
The final temperature is 10.1 degrees Fahrenheit
Mel works as a waiter. He uses the linear expression 4x+5 to calculate his hourly earning , in dollars based on the number of tables x, that he serves. What is the fewest number of tables he must serve per hlur in order to earn more that $25 per hour ?
Answers
Mel must serve a minimum of 6 tables per hour to earn more than $25 per hour.
Here, we are given that Mel uses the linear expression (4x + 5) to calculate his hourly earning, in dollars. Here x = number of tables served.
If he wants to earn $25 per hour then the value of the linear equation must be equal to 25. This means-
4x + 5 = 25
4x = 25 - 5
4x = 20
x = 20/ 4
x = 5
Now, if he wants to earn more than $25 per hour, he must serve more than 5 tables. This implies that he must as least serve 6 tables.
Thus, Mel must serve a minimum of 6 tables per hour to earn more than $25 per hour.
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QUESTION 1 Determine the general solution of: 2 sin x. cos x = COS X
Answers
Starting with the given equation: 2 sin x cos x = cos x
By dividing both sides by cos x, we may simplify: 2 sin x = 1
Dividing both sides by 2:
sin x = 1/2
The values of x that fulfil sin x = 1/2 must now be found, and they are:
x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.
Therefore, the general solution is:
x = π/6 + 2πn or
x = 5π/6 + 2πn, where n is any integer.
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Given A = {10, 11, 12, 13}, B = {10, 12, 14, 16}, and C = {7, 8, 9, 10, 11}, find
A ∪ B
A ∩ B
A ∪ C
A ∩ C
B ∪ C
B ∩ C
Answers
The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:
A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.
A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.
A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.
A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.
B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.
B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.
Finally, performing the remaining operations:
(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.
(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.
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If the measure of angle ABD is 100, what is the measure of angle ABC
Answers
i dont know. Im sorry about that.
Krista designs quilts using the pattern shown. The table of values describes the shaded area of the pattern in square units, y, as a function of the length of a side,X units. Which equation describes this relationship?
Answers
The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²
Modeling relationship between two variablesSide length, x = 1,3,4,5,8
Shaded Area, y = 0.5, 4.5, 8, 12.5, 32
The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c
a = 0.5 ; b = 0 ; c = 0
Therefore, the quadratic function can be written as y = 0.5x²
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4/3 (3x-12)=2x+8 what is x
Answers
The answer is, X = 12.
hope it helps.
Answer:
x = 12
Step-by-step explanation:
simlify 4/3 * (3x-12)
4x - 16 = 2x + 8
combine like terms, so subtract 2x by 4x
2x - 16= 8
then finish combining like terms, so 16 plus 8
2x = 24
divide 24 by 2
x = 12
Which of the following has imaginary solutions?
x ^ 2 + 3x - 5 = 0
x ^ 4 - 5x ^ 2 + 3 = 0
2x ^ 2 - 6x = - 7
- 3x ^ 2 = - 5
Answers
2x² - 6x = -7 equation has imaginary solutions
To determine if an equation has imaginary solutions, we can examine the discriminant of the quadratic equation
x² + 3x - 5 = 0
a = 1, b = 3, c = -5
Discriminant = (3)² - 4(1)(-5) = 9 + 20 = 29
The equation has two real solutions
x⁴ - 5x ^ 2 + 3 = 0
This equation is a quartic equation, not a quadratic equation. Quartic equations can have both real and imaginary solutions
2x² - 6x = -7
2x^2 - 6x + 7 = 0
a = 2, b = -6, c = 7
Discriminant = (-6)²- 4(2)(7) = 36 - 56 = -20
Since the discriminant (-20) is negative, the equation has two complex (imaginary) solutions.
-3x² = -5
Dividing both sides by -3, we get:
x²= 5
a = 1, b = 0, c = -5
Discriminant = 0² - 4(1)(-5) = 20
The equation has two real solutions.
Hence, 2x² - 6x = -7 equation has imaginary solutions
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please help me will give u extra points :)
•
Answers
Answer:
Ok
Step-by-step explanation:
18+ 4(28) use the properites of operations to evaluate this expressions?
Answers
The value of the expression 18 + 4(28) will be 130.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ 18 + 4(28)
Simplify the expression, then the value of the expression will be
⇒ 18 + 4 x (28)
⇒ 18 + 4 x 28
⇒ 18 + 112
⇒ 130
Thus, the value of the expression 18 + 4(28) will be 130.
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